Mach Wave Angle Calculator

Mach wave is a pressure wave travelling with the speed of sound caused by a slight change of pressure added to a compressible flow. This calculator computes the Mach wave angle.
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CalculationInputs﻿﻿M
:3.00​
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Outputs﻿﻿μ (rad)
:0.34​
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﻿﻿μ (deg)
:19.47​
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μ=sin⁡−1(1M)\mu = \sin^{-1}(\frac{1}{M})μ=sin−1(M1​)
Where:
μ is the angle formed between the Mach wave wavefront and a vector that points opposite to the vector of motion, in radians or degrees 
﻿﻿M
 is the Mach number (dimensionless)
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ExplanationIn fluid dynamics, a Mach wave is a type of pressure wave that travels at the speed of sound. It is caused by a slight change in pressure within a compressible flow. When multiple Mach waves combine in supersonic flow, they can create a shock wave. If enough Mach waves are present at a location, this shock wave is called a Mach stem or Mach front. By spacing out the production of Mach waves, it is possible to achieve shockless compression or expansion in a supersonic flow. This is known as isentropic compression in supersonic flows. 
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Shockwave created by a bullet
Read more on Mach waves
A Mach wave moves across the flow at a specific angle called the Mach angle, ﻿μ
. The Mach angle is the angle between the Mach wavefront and a vector that points opposite the vector of motion. 
👉To calculate the Mach angle, you only need the Mach Number. You can use our Mach Number Calculator.
Derivation of ﻿μ
﻿Minor disturbances are transmitted downstream within a cone for supersonic and hypersonic flows. The green lines in the figure below depict the two-dimensional edge of the cone, moving at velocity ﻿v
. Sound waves strike the edge of the cone at a right angle, and the speed of the sound wave is denoted by the letter ﻿a
, where ﻿v
 is greater than ﻿a
.
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Mach wave and Mach angle
From trigonometry, the sine of the cone angle ﻿μ
 is equal to:
﻿
sin⁡(μ)=av\sin(\mu) = \dfrac{a}{v}sin(μ)=va​
But the ratio of ﻿v
 to a is the Mach number of the flow, that is:
﻿
M=vaM=\dfrac{v}{a}M=av​
Therefore, we can determine that the cone angle ﻿μ
 equals:
﻿
sin⁡(μ)=1M\sin(\mu) = \dfrac{1}{M}sin(μ)=M1​
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→μ=sin⁡−1(1M)\rightarrow\mu = \sin^{-1}(\dfrac{1}{M})→μ=sin−1(M1​)
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Related ResourcesMach Number Calculator
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Mach Wave Angle Calculator

Calculation

Inputs

Outputs

Explanation

Read more on Mach waves

Derivation of ﻿μ﻿

Related Resources

Derivation of

$μ$
